Question: $\lim_{x\to 0}\csc(x)=?$ Choose 1 answer: Choose 1 answer: (Choice A) A $-1$ (Choice B) B $0$ (Choice C) C $1$ (Choice D) D The limit doesn't exist.
Answer: $\csc(x)$ is continuous on all points in its domain. Therefore, if $x=0$ is within the domain of $\csc(x)$, we can find $\lim_{x\to 0}\csc(x)$ by direct substitution. $x=0$ is not in the domain of $\csc(x)$ : $\begin{aligned} \csc\left(0\right)&=\dfrac{1}{\sin\left(0\right)} \\\\ &=\dfrac{1}{0} \end{aligned}$ Since direct substitution ends with $\dfrac{1}{0}$, we know that $\lim_{x\to 0}\csc(x)$ doesn't exist.